trabajo fin de grado desarrollo de una antena de …

Universidad Autónoma de Madrid

Escuela politécnica superior

Grado en Ingeniería de Tecnologías y

Servicios de Telecomunicación

TRABAJO FIN DE GRADO

DESARROLLO DE UNA ANTENA

DE BOCINA CORRUGADA PARA

UN RADAR MONOPULSO EN LA

BANDA L

Author: Andreea Simona Palade

Supervisor: Korbinian Schraml

Co-Supervisor: José Luis Masa Campos

Desarrollo de una antena de bocina corrugada para un radar monopulso en la banda L

2

DEVELOPMENT OF A

CORRUGATED HORN ANTENNA

FOR MONOPULSE RADAR AT

L-BAND

Author: Andreea Simona Palade

Supervisor: Korbinian Schraml

Co-Supervisor: José Luis Masa Campos

IHF - Institute of High Frequency Technology

RWTH Aachen University

Germany

December 2017

i

Abstract

Abstract

The mono-pulse tracking and imaging radar (TIRA) is a space observation radar which usesa four-pyramidal-horns array to feed the re�ector of the system. The radiation pattern of thearray has too high side lobes, causing a high radiation power below the safety limits. The aimof this thesis is to study if with four-corrugated-horns array, lower side lobes can be achieved.

First of all, the design of a corrugated horn antenna is carried out. The antenna operates inL-band, at 1.3 GHz. As the ultimate purpose of the horn is being used in a monopulse radar,the basis of this type of radar are �rstly described. In order to correctly estimate the dimensionsof the antenna, the theoretical background of corrugated horns is described.

Following, the development of the antenna is detailed. In the �rst place, the sizes of thehorn are estimated, supposing that it is optimum. Secondly, the dimensions of the corrugationsare calculated, including their depth. It is important to de�ne a coordinate system for thecorrugations in order to generate the horn in CST, and compute their coordinates and thecoordinates of the waveguide.

Regarding the depths of the corrugations, the combination of depths that maximize theperformance of the system is attempted to �nd. To this aim, a parameter sweep is performedfor the depth of each corrugation. The results of this process are compared with the results of agenetic algorithm optimization. Then, the in�uence that the number of corrugations have on theperformance of the system is analized. For this purpose, two new horn models are developed:one with the minimum number of corrugations possible and another one with more corrugationsthan the �rst one. These three systems are analized and compared.

Finally, three antennas arrays are generated: one for each type of horn. The performance ofeach system is analized and the radiation patterns are compared with the radiation patterns ofthe TIRA reference.

Resumen

El radar monopulso TIRA (Tracking and Imaging Radar) es un radar de observación espacialen el que se usa un array formado por cuatro antenas de bocina piramidal para alimentar elre�ector del sistema. Este radar tiene una limitación: su potencia de radiación está por encimade los límites de seguridad débido a que el nivel de los lóbulos secundarios del diagrama deradiación del array es muy alto. Este Trabajo Fin de Grado estudia si es posible reducir el nivelde los lóbulos secundarios del diagrama de radiación del array, empleando una antena de bocinacónica corrugada para el array.

En primer lugar, se describen las principales características de un radar monopulso y de unaantena de bocina cónica corrugada. Después, se lleva a cabo el diseño de la bocina, teniendo encuenta que ésta opera en la banda L, a 1.3 GHz.

iii


A continuación, se explica detalladamente el desarrollo de la antena. En primer lugar, secalculan las dimensiones de la antena de bocina suponiendo que es óptima. En segundo lugar,se de�ne un sistema de coordenadas para las corrugaciones y se calculan sus dimensiones.

En cuanto a la profundidad de las corrugaciones, se busca la commbinación de profunidadesque maximiza el rendimiento del sistema. Esto se hace de dos formas: manual, mediante unbarrido para cada parámetro, y de forma automática mediante una optimización empleando elalgoritmo genético. Después, se estudia que in�uencia tiene el número de corrugaciones sobre elrendimiento del sistema. Para ello, se desarrollan otras dos bocinas: una con el mínimo númerode corrugaciones posible, y otra, con más corrugaciones que la primera.

Finalmente, se generan tres arrays de antenas: uno para cada tipo de bocina. El diagrama deradiación de cada array se analiza y se compara con el diagrama de radiación del array empleadoen el radar TIRA.

Key words

Monopulse Radar, TIRA, Antenna, Horn, Conical Horn, Corrugated Horn, Corrugations, Ge-netic Algorithm, Optimization, Array, Radiation Pattern.

Palabras clave

Radar Monopulso, Antena, Antena de bocina, Bocina cónica, Bocina corrugada, Corrugaciones,Algoritmo Genético, Optimización, Array, Diagrama de Radiación.

iv

Acknowledgement

I would �rst like to thank to my thesis supervisior Korbinian Schraml, for giving me thechance to do this Bachelor thesis, for all the new things I have learned and for all his supportand advices.

Thanks to Cosme Culotta-López to make it possible to come to Aachen, for giving me allthe information I needed in order to organize and carry out this exchange program.

Thanks to José Luis Masa Campos for being my co-supervisor and for helping me with theadministrative process.

Furthermore I would like to thank to Professor Heberling for giving me the opportunity todo this project in the Institut für Hochfrequentztechnik in RWTH Aachen University.

Finally, I would like to thank to my loved ones, to my family and friends who have supportedme throughout all these years, for encouraging me, for being by my side, for never giving up onme and for never letting me to give up.

v


vi

Contents

List of Figures ix

List of Tables xi

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 State of the art 3

2.1 Monopulse radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Phased Antenna Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.2 Antenna Feeds on Monopulse Radar . . . . . . . . . . . . . . . . . . . . . 5

2.2 Aperture antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Horn antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3.2 Conical horn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.3 Corrugated horn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Antenna Design 13

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 Conical Horn Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3 Corrugations Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.3.1 Depths Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3.2 Number of corrugations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4 Array Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.4.1 Array formed by four 10-corrugations horns . . . . . . . . . . . . . . . . . 35



4 Conclusions 41

vii


Appendix 1: Corrugations Coordinate System i

Appendix 2: Step-by-step tuning vii

Appendix 3: Tables containing the values of the depths of the corrugations xxiii

viii CONTENTS

List of Figures

1.1 Insight into space observation radar TIRA . . . . . . . . . . . . . . . . . . . . . . 1

2.1 Partial antenna patterns for amplitude sum-and-di�erence monopulse system. . . 4

2.2 Determinating angular coordinates for phase-comparison monopulse system. . . . 4

2.3 Block diagram of a monopulse system . . . . . . . . . . . . . . . . . . . . . . . . 4

2.4 A four-horn irradiator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.5 Excitation diagram of a four-horn irradiator . . . . . . . . . . . . . . . . . . . . . 6

2.6 Aperture Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.7 Horn Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.8 Conical horn geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.9 E-plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.10 H-plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.11 Diameter of horn aperture 2A(wavelengths) . . . . . . . . . . . . . . . . . . . . . 9

2.12 Corrugated pyramidal horn with corrugations in the E-plane . . . . . . . . . . . . 10

2.13 Types of corrugations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.14 Scalar horn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1 View of the horn in CST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 Gain vs Corrugations depth before the aperture . . . . . . . . . . . . . . . . . . . 16

3.3 3-dB Beamwidth vs Corrugations depth before the aperture . . . . . . . . . . . . 17

3.4 Gain vs Depth of the corrugations at the aperture . . . . . . . . . . . . . . . . . 18

3.5 3-dB Beamwidth vs Depth of the corrugations at the aperture . . . . . . . . . . . 18

3.6 Gain and Beamwidth of the second corrugation with respect to the Depth . . . . 20

3.7 Gain and Beamwidth of the twelfth corrugation with respect to the Depth . . . . 21

3.8 S11 Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.9 Radiation pattern of the copolar component of the E-plane . . . . . . . . . . . . 22

3.10 Radiation pattern of the crosspolar component of the E-plane . . . . . . . . . . . 23

3.11 Radiation pattern of the copolar component of the H-plane . . . . . . . . . . . . 23

3.12 Radiation pattern of the crosspolar component of the H-plane . . . . . . . . . . . 24

3.13 S11 Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

ix






3.18 S11 Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28





3.23 S11 Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31





3.28 Radiation patterns of the copolar components of the E-plane of the horns arrayand the TIRA Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.29 Radiation patterns of the copolar components of the H-plane of the horns arrayand the TIRA Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.30 Radiation pattern of the copolar components of the E-plane of the horns arrayand the TIRA Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37


3.32 Radiation patterns of the copolar component of the E-plane of the horns arrayand the TIRA Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38


1 Cross section of the horn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

2 Coordinates of the �rst two corrugations. . . . . . . . . . . . . . . . . . . . . . . ii

3 Coordinates de�ned by points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

3 Cross section of the waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

4 Cross section of the aperture of the horn . . . . . . . . . . . . . . . . . . . . . . . vi

5 Gain vs Depth of the second corrugation . . . . . . . . . . . . . . . . . . . . . . . vii

6 3-dB Beamwidth vs Depth of the the second corrugation . . . . . . . . . . . . . . viii

7 Gain vs Depth of the third corrugation . . . . . . . . . . . . . . . . . . . . . . . . ix

8 3-dB Beamwidth vs Depth of the third corrugation . . . . . . . . . . . . . . . . . ix

9 Gain vs Depth of the fourth corrugation . . . . . . . . . . . . . . . . . . . . . . . x

10 3-dB Beamwidth vs Depth of the fourth corrugation . . . . . . . . . . . . . . . . x

x LIST OF FIGURES


11 Gain vs Depth of the �fth corrugation . . . . . . . . . . . . . . . . . . . . . . . . xii

12 3-dB Beamwidth vs Depth of the �fth corrugation . . . . . . . . . . . . . . . . . xii

13 Gain vs Depth of the sixth corrugation . . . . . . . . . . . . . . . . . . . . . . . . xiii

14 3-dB Beamwidth vs Depth of the sixth corrugation . . . . . . . . . . . . . . . . . xiii

15 Gain vs Depth of the seventh corrugation . . . . . . . . . . . . . . . . . . . . . . xiv

16 3-dB Beamwidth vs Depth of the seventh corrugation . . . . . . . . . . . . . . . . xv

17 Gain vs Depth of the eighth corrugation . . . . . . . . . . . . . . . . . . . . . . . xvi

18 3-dB Beamwidth vs Depth of the eighth corrugation . . . . . . . . . . . . . . . . xvi

19 Gain vs Depth of the ninth corrugation . . . . . . . . . . . . . . . . . . . . . . . . xvii

20 3-dB Beamwidth vs Depth of the ninth corrugation . . . . . . . . . . . . . . . . . xvii

21 Gain vs Depth of the tenth corrugation . . . . . . . . . . . . . . . . . . . . . . . . xviii

22 3-dB Beamwidth vs Depth of the tenth corrugation . . . . . . . . . . . . . . . . . xviii

23 Gain vs Depth of the eleventh corrugation . . . . . . . . . . . . . . . . . . . . . . xix

24 3-dB Beamwidth vs Depth of the eleventh corrugation . . . . . . . . . . . . . . . xx

25 Gain vs Depth of the twelfth corrugation . . . . . . . . . . . . . . . . . . . . . . . xxi

26 3-dB Beamwidth vs Depth of the twelfth corrugation . . . . . . . . . . . . . . . . xxi

LIST OF FIGURES xi


xii LIST OF FIGURES

List of Tables

3.1 Design Speci�cations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 Conical horn dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3 Waveguide dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.4 Corrugations dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.5 Antenna Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.6 Antenna characteristics after optimization . . . . . . . . . . . . . . . . . . . . . . 27

3.7 10-corrugations horn characteristics before optimization . . . . . . . . . . . . . . 31

3.8 14-corrugations horn characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.9 Horns characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

1 Coordinates of the 12 corrugations . . . . . . . . . . . . . . . . . . . . . . . . . . iv

2 Auxiliary parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

3 Depth values for the simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

4 Corrugations Depths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii

5 Depths of the corrugations after the �rst genetic algorithm optimization . . . . . xxiii

6 Corrugations Depths after the second genetic algorithm optimization . . . . . . . xxiv

7 Corrugations dimensions for a 10-corrugations horn . . . . . . . . . . . . . . . . . xxv

8 Depths of the 10 corrugations after optimization . . . . . . . . . . . . . . . . . . xxvi

9 Corrugations dimensions for a 14-corrugations horn . . . . . . . . . . . . . . . . . xxvii

xiii


xiv LIST OF TABLES

1Introduction

1.1 Motivation

The mono-pulse tracking and imaging Radar (TIRA) is a space observation radar located atthe Fraunhofer Institute for High Frequency Physics and Radar Techniques in Germany. Thesystem serves as the central experimental facility for the development and investigation of radartechniques for the detection and reconnaissance of objects in space. TIRA can measure the orbitwith high precision or produce a high resolution image of objects such as satellites.

The radar operates in L-band for tracking and debris detection at 1.3 GHz. For imaging itoperates in Ku-band at 16.7 GHz. The system uses a 34 metres diameter horn antenna to feeda re�ector (Figure 1.1). The antenna can be turned 360°in azimuth and 90°in elevation [1].

The antenna system used to feed the re�ector is a 2x2 array formed by four smooth-wallpyramidal horns. This array has a drawback: the side lobe level of its radiation pattern is toohigh. The radiation power is too high and it is below the safety limits. This thesis studies ifwith an array formed by four corrugated horns lower side lobes can be achieved and therefore ifthere is possible to transmit more power within the safety limits.

Figure 1.1: Insight into space observation radar TIRA

Source: [1]

1


1.2 Goals

The main goal of this thesis is the design of a corrugated horn antenna. For this purpose,the dimensions of the horn antenna are calculated in the �rst place. Then, a coordinate systemis de�ned in order to correctly place the corrugations in the plane and their dimensions, as theirlength and the distance between them, are computed.

The next goal is to estimate the depths of the corrugations that maximize the gain of thesystem. To achieve this, several parameter sweeps and two genetic algoritm optimizations havebeen done.

Following, it is analized what number of corrugations should have the horn to achieve abetter system performance.

Finally, three antenna arrays are generated and the last goal is to compare the radiationpatterns of this arrays with the radiation patterns of the TIRA Reference.

1.3 Outline

This document has the following outline:

• Chapter 1: Introduction - In this chapter, the motivation, the goals and the outlines ofthe thesis are described.

• Chapter 2: State of the art - First, the fundaments of the monopulse radar are introducedin this chapter. Secondly, the types of aperture antennas are listed and next, horn antennasbasis are explained. Then, conical and corrugated horn antennas are gone into in moredetail, since all the concepts presented are used throughout the document.

• Chapter 3: Antenna design - In this chapter all the procedures that have been followedin order to generate the antenna are described step by step. First of all, the conical horndesign, then the corrugations design, including their coordinate system and their depths.After that, the impact which the number of corrugations have on the horn is analized, andtwo new horn models are proposed. Next, an array is generated and �nally a comparisonbetween the radiation patterns of the array and the TIRA reference is made.

• Chapter 4: Conclusions - This chapther draws the conclusions based on these analysis andarises the future work.

2 CHAPTER 1. INTRODUCTION

2State of the art

2.1 Monopulse radar

A radar system is often used for tracking. It determinates the current and future position ofa target by measuring its coordinates [2]. With the monopulse radar, the angular position of atarget can be obtained from only one pulse, as its name indicates. In order to �nd out the direc-tion to target, two important techniques have been developed: the amplitude-comparisonmethod and the phase-comparison method.The amplitude-comparison monopulse uses two intersecting antenna radiation patternsseparated by an angle ±θs from the equisignal direction. Both sum and di�erence patterns areused on reception, while only the sum pattern is used on transmission . The sum signal is usedfor range measurment. If the amplitudes of the antennas patterns are rested, the result will bethe magnitude of the target deviation from the equisignal direction, and its sign indicates thedirection of the displacement. The di�erence will be zero when the equisignal direction and thetarget coincide [2], [3].As explained in [3], additions and subtractions between signals and scalar multiplications aremade by converters after the signals have been ampli�ed. The converters and ampli�ers arecontained in the angular discriminator. There are three types of angular discriminators: am-plitude discriminator, responding only to amplitude ratios, phase discriminator reactingonly to phase ratios and sum-di�erence discriminator, used for both amplitude and phaseratios and also for adding and substracting operations. In Figure 2.1 are shown the raddiationpatterns of an amplitude-comparison monopulse system with sum-and-di�erence angle discrim-inator. The reference system axis for the measurment is θ0. The main beams directions of thetwo antennas are separated by the angle θs. These patterns are added and subtracted. Theresult of the subtraction is ∆θ, the magnitude of the angle error [4].

3


Figure 2.1: Partial antenna patterns for amplitude sum-and-di�erence monopulse system.

Source: [4]

The phase-comparison monopulse compares the phases of the signals received by twoantennas in order to determine the direction to target. The far�eld radiations have equal mag-nitude in space, hence the re�ected signals have the same amplitude, but di�erent phase. Figure2.2 shows two antennas separated by a distance d. θ is the angle between the line of sight ofthe target and the x -axis. The line joining the two antennas is perpendicular to the x -axis. Thedistance from Antenna 1 to the target is R1 = R+ d

2 sin θ and the distance from Antenna 2 to

the target is R2 = R− d2 sin θ. The phase di�erence between the signals is ∆ϕ = 2π

λ d sin θ [2].

Figure 2.2: Determinating angular coordinates for phase-comparison monopulse system.

Source: [3]

A monopulse system consists of three basic elements which appear in Figure 2.3. The angle-data transmitter provides information about the angular position of the target. It is the antennaof the monopulse system. The information converter converts the signal parameter ratios, andthe angular discriminator provides the angle measurment [3].

Figure 2.3: Block diagram of a monopulse system

Source: [3]

4 CHAPTER 2. STATE OF THE ART


2.1.1 Phased Antenna Arrays

A phased antenna array is a set of antennas which generates a radiation pattern whose shape anddirection depends on every single element of the array. The main advantage of using antennasarrays in radar systems is that they o�er the possibility to control the direction of the radiationby varying the relative phases of each individual antenna. This can be done through electroniccontrol.The distance between elements should be λ

2 in order to obtain the smallest side lobes. If the

distance is greater than λ2 , grating lobes may appear.

If the radiation pattern of an array has only one beam, phase switchers can be added at theend of each antenna. One additional beam will appear for every phase switcher inserted andthe result will be a multi-beam antenna. For an amplitude-comparison monopulse system, afterbeing ampli�ed the signals are fed to two phase switchers, forming two beams. The signals fromthe outputs of the phase switchers are fed to the summator. For a phase-comparison monopulsesystem, two radiation patterns are formed by adding the signals from each half of the array. [3].

2.1.2 Antenna Feeds on Monopulse Radar

For an antenna array feeding a re�ector formed by four horns, the direction to target can bedeterminated by comparing paired sums of signals. For instance, with the irradiator arrangementshown in Figure 2.4, the greatest propagation is obtained. If the sum of signals (1+2) is comparedwith (3+4), elevation will be measured, and if (1+3) is compared with (2+4), azimuth will bemeasured.

Figure 2.4: A four-horn irradiator

Source: [3]

The horns are excited according to the diagram showed in Figure 2.5. The waveguide bridgesare used at the points indicated in the diagram. On the �rst two bridges, the signals (1,3) and(2,4) are summed in pairs and then added in bridge III forming the sum signal

∑. In bridge

III the sum of the signals (2,4) is subtracted from the sum of the signals (1,3), forming thedi�erence signal ∆ with respect to azimuth. The di�erence signal with respect to elevation isobtained by adding in the bridge IV the di�erence of signals (1,3) and (2,4), obtained on the�rst two bridges. This gives the required result because the system is linear and the associativelaw is applicable to it (1− 3) + (2− 4) = (1 + 2)− (3 + 4). In order to form the sum radiationpattern, the shaping circuit of the irradiating system excites in phase all four-horns. In order toobtain the most optimal radiation, horn dimensions are selected so that in the formation of thesum beam the antenna has maximum ampli�cation with uniform irradiation of the mirror [3].

CHAPTER 2. STATE OF THE ART 5


Figure 2.5: Excitation diagram of a four-horn irradiator

Source: [3]

2.2 Aperture antennas

An aperture antenna is an antenna with an aperture at the end through which radiates energyin one speci�c direction. It is most commonly used at microwave frequencies.The aperture can be square, rectangular, circular, elliptical, or it can take any other shape.Some apertures are delimited by conductive metal walls, as the slot antenna in Figure 2.6a orthe horn antenna in Figure 2.6b. Other ones, such as re�ector antennas in Figure 2.6c and lensantennas in Figure 2.6d, are de�ned as a portion of a �at front surface in which the �elds of thewave collimated by it takes signi�cant values.Aperture antennas are most commonly used for aerospace applications because they can beinserted into the spacecraft or aircraft surface [5], [6].This thesis is focused on a horn antenna.

(a) Slot Antenna (b) Horn Antenna

(c) Re�ector Antenna (d) Lens Antenna

Figure 2.6: Aperture Antennas

Source: [6]



2.3 Horn antennas

2.3.1 Introduction

The horn antenna can be de�ned as a section of waveguide where the open end is �ared in orderto adapt the radiant medium to the feeding waveguide [6]. The �ared portion can be square,rectangular, or conical and its type, direction, and amount can have a deep e�ect on the generalperformance of the element as a radiator.The maximum radiation corresponds with the axis of the horn. The horn is usually fed with awaveguide, which can be rectangular or circular. In Figure 2.7 di�erent types of horn antennaare shown.

(a) E-plane sectoral horn (b) H-plane sectoral horn

(c) Pyramidal horn (d) Conical horn

Figure 2.7: Horn Antennas

Source: [7]

The horn antennas are very popular for space and ground-based antenna systems becausethey are easy to manufacture and RF losses are low even at millimeter and submillimeter fre-quency ranges. They can reach high gains and high bandwidths, they are easy to excite andvery versatile.The horn is most commonly used to feed re�ectors and lenses. It is a common element of phasedarrays and serves as a universal standard for calibration and gain measurements of other highgain antennas.The horn is used in large radio astronomy, satellite tracking, and communication dishes installedthroughout the world [5].



2.3.2 Conical horn

Conical horns are usually feed with circular waveguides. A big advantage of the circular waveg-uide is that it allows any type of polarization. The geometry of the conical horn is shown inFigure 2.8, where a is the radius of the circular waveguide aperture, Rc is the slant radius, morespeci�cally the distance between the waveguide-horn junction and the sides of the horn, Lc is theaxial length, in other words the distance between the center of the aperture and the junction,A is the radius of the aperture and γc is the semi�are angle [8].

Figure 2.8: Conical horn geometry

Source: [7]

The maximum quadratic phase error is s = A2

2λ0Lc. The normalized radiation pattern for

the E-plane is illustrated in Figure 2.9 and for the H-plane in Figure 2.10, both without the

obliquity factor1+cos θ

2 [6].

Figure 2.9: E-plane

Source: [7]



Figure 2.10: H-plane

Source: [7]

In Figure 2.11 is shown the directivity of a conical horn as a function of the aperture diameterand for di�erent axial horn lengths. As it can be observed, as the �are angle increases, thedirectivity of the horn increases and after it hits a maximum point, it starts to decrease due tothe dominance of the quadratic phase error at the aperture [7].

Figure 2.11: Diameter of horn aperture 2A(wavelengths)

Source: [7]

The directivity of a conical horn is optimum when its radius is equal to A =√3λ0Lc

2 , whichcorresponds to a maximum quadratic phase error s = 3

8 and an aperture e�ciency around 51%[7]. If the aperture of the horn is �at and uniform illuminated, the aperture e�ciency will be of



100% [6]. Consequently, the gain will be equal to the directivity: G0 = D0 = 4πλ20Aaper, where

Aaper is the area of the aperture. For a circular aperture, Aaper = πA2, where A is the radius

of the aperture. Hence, the gain will be: G0 = 4π2A2

λ20. Therefore, the directivity of the horn

increases when the radius of the aperture increments.

2.3.3 Corrugated horn

When the smooth-wall horn is used as a feeding element for a re�ector, it leads to astigma-tism, which consists in unequal phase centers in orthogonal planes. For dual linear or circularpolarization, the horn aperture must be square or circular and the beamwidths in the E-planeand H-plane are not equal. Furthermore, the sidelobes in the E-plane are higher than in theH-plane. Finally, the di�raction of the E-plane walls causes backlobes. All these problems canbe eliminated by corrugating the walls [8].Concerning the e�ciency, with smooth-wall horns aperture e�ciencies of 50-60% can be ob-tained, while with corrugated horns e�ciences of the order of 75-80% can be achieved. Com-pared with a smooth-wall horn, a corrugated horn has larger 3 -dB beamwidth, a lower 10 -dBbeamwidth and lower levels of the minor lobes and back lobes. The corrugations placed onthe walls perpendicular to the E �eld of a horn transform the electric �eld distribution in theE-plane from uniform at the waveguide-horn junction to cosine at the aperture.Figure 2.13 shows a corrugated pyramidal horn, with corrugations in the E-plane walls. In theH-plane, normaly there are not corrugations, as di�ractions at the edges of the aperture in thisplane are insigni�cant. As showed in Figure, there are two types of corrugations: perpendicularto surface and perpendicular to axis[7]. In Figure 2.14 a conical corrugated horn, also denomi-nated scalar horn can be seen.In this thesis a conical corrugated horn with corrugations perpendicular to axis is developed.

(a) Corrugated pyramidal horn

(b) E-plane

Figure 2.12: Corrugated pyramidal horn with corrugations in the E-plane

Source: [7]



(a) Corrugations perpendicular to surface

(b) Corrugations perpendicular to axis

Figure 2.13: Types of corrugations

Source: [7]

Figure 2.14: Scalar horn

For an e�cient design, it is necessary to use 10 or more corrugations per wavelength[7].According to [7], to simplify the analysis of an in�nite corrugated surface, it will be assumedthat:

1. The teeth of the corrugations are very thin.

2. Re�ections from the base of the corrugation are only those of a TEM mode.

Moreover, the second assumption is valid only if the width of the corrugations w is smallenough compared to the free-space wavelength λ0 and the depth of the corrugations d. Theassumption will be: w < λ0

10 .

If a corrugated surface complies with the speci�ed assumptions, its aproximate surface reac-tance will be:

X = ww+t

√µ0ε0

tan(k0d) , when ww+t∼= 1, which can only be satis�ed if t < w

10 .

It is important that the surface reactance of corrugated surfaces is capacitive, to annulthe tangential magnetic �eld parallel to the edge at the wall. Consequently, these surfaceswill not support surface waves, will prevent illumination of the E-plane edges, and will reducedi�ractions. This can be accomplished if λ0

4 < d < λ02 . If d < λ0

4 or d > λ02 , the surface

reactance will be inductive, and if 3λ02 < d < λ0 will be capacitive again, but this interval is

not so commonly used. Furthermore, the corrugations need to be λ04 at the aperture since a λ0

4corrugation depth balances TM11 and TE11 modes coexisting and gives better results. Before



the aperture the corrugations depth must be higher than a quarter-wavelength, otherwise therewill be mismatching in the transition region, where the TM11 mode is generated from the TE11

mode. On the other hand, if depths are approximately λ02 , their in�uence on the matching will

be negligible [8]. Moreover, the cuto� depth depends on the corrugation width w, but its e�ectis insigni�cant if w < λ0

10 and λ04 < d < λ0

2 [7].

In addition, if the corrugations are very close to the waveguide-horn junction, they will a�ectthe impedance and VSWR of the antenna. In order to avoid this, the �rst corrugation must beplaced at a small distance away from the junction [7].


3Antenna Design

3.1 Introduction

In this chapter, the antenna design is described step by step. The design speci�cations are shownin Table 3.1. The L-band goes from 1 to 2 GHz and the central frequency of the system is 1.3GHz.First, the dimensions of the horn as the axial length, the radius of the aperture, the slant radius,the semi�are angle and the dimensions of the waveguide are calculated. Secondly, the dimen-sions of the corrugations are estimated and then their coordinate system, more speci�cally, thecoordinates of each point of each corrugation. Continuing, a series of simulations are performedin order to �nd the depths which maximize the gain of the system. Next, the e�ect that thenumber of corrugations have on the system is studied. To this aim, two more horns are created:one with the minimum number of corrugations possible(10), and another one with two more cor-rugations than the �rst one. Finally, three arrays are generated, one for each type of corrugatedhorn. In the end, the resulting radiation patterns are compared with the TIRA reference.

Table 3.1: Design Speci�cations

Central Frequency 1.3 GHz

Gain 15 dBi

Thickness of the Metal 2.3 mm

13


3.2 Conical Horn Design

The design which has been realized is optimum in order to achieve the maximum directivity. InFigure 2.8 the geometry of a conical horn was shown. Considering what has been explained inthe section 2.3.2 and the design speci�cations showed in Table 3.1, the dimensions of the hornhave been calculated such as indicated in Table 3.2.

Table 3.2: Conical horn dimensions

Parameter Symbol Formula Result Units

Axial Length LcG0λ03π2 240.30 mm

Aperture Radius A

√3λ0Lc

2 201.37 mm

Slant Radius Rc√L2c +A2 313.52 mm

Semi�are Angle γc atan( ALc) 39.96 degrees

The circular waveguide is determinated by a length and a radius. In a �rst approach, arandom value proportional to the sizes of the horn was choosen for the length. Respecting theradius of the waveguide, it must be considered that the cuto� frequency for a circular waveguide

is fc =1.8412c

2πa , where c is the speed of light within the waveguide in metres per second and a

is the internal radius of the circular waveguide in metres. A radius value must be found, so thatthe central frequency of the system stays between the cuto� frequency of the lowest mode (H11)and the cuto� frequency of the second mode (E01). For instance, if the radius of the waveguideis 80 mm, the cuto� frequency of the lowest mode is 1.09 GHZ and the cuto� frequency of thesecond mode is 1.3061*1.09 GHz=1.42 GHz.

Table 3.3: Waveguide dimensions

Parameter Symbol Value Units

Waveguide Length Length_wg 120 mm

Waveguide Radius Rad_wg 80 mm

14 CHAPTER 3. ANTENNA DESIGN


3.3 Corrugations Design

According to section 2.3.3, in Table 3.4 the dimensions of the corrugations have been summarizedand calculated in function of λ0. It is assumed that all the corrugations have the same width(w),and also that they all have the same teeth(t). As the horn must have at least 10 corrugations,as a �rst approach 12 corrugations have been choosen.

Table 3.4: Corrugations dimensions


Width of the corrugations wλ010 22.5 mm

Depth of the corrugations at the aperture daperλ04 56.25 mm

Depth of the corrugations before the aperture d 0.4λ0 90 mm

Teeth of the corrugations tw10 2.25 mm

Distance from the waveguide-horn junction distance Lc − (12t+ 12w) 16.52 mm

(a) Lateral view (b) Front view

(c) Cross section view

Figure 3.1: View of the horn in CST

CHAPTER 3. ANTENNA DESIGN 15


3.3.1 Depths Design

In this section several simulations are performed in order to �nd the combination of depths thatmaximizes the gain of the antenna. The gain variation with the depth and the 3-dB beamwidthin the E-plane are evaluated for each step.First, it is assumed that the depth of the �rst corrugation starting from the aperture is λ0

4 , asa quarter-wavelength corrugation depth balances the modes coexisting. In the �rst simulation,in order to observe the behaviour of the system, a parameter sweep is performed for the depthsof the rest of the corrugations, supposing that they are equal to each other. In the secondsimulation, a parameter sweep for the depth at the aperture is performed to demonstrate thatthe quarter-wavelength corrugation is the best choice. Next, an optimization using the geneticalgorithm is runned in order to automatically �nd the depths that maximize the gain. As theoptimization failed, for each corrugation depth a parameter sweep is performed to study if ahigher gain can be achieved.

Equal depths before the aperture

For this simulation it is assumed that the depth of the corrugation at the aperture (daper) isequal to λ0

4 and that the rest of the corrugations (from D2 to D12) have the same depth. A

parameter sweep from λ04 = 56.25 mm to λ0

2 = 112.25 mm is performed in order to �nd outwhat depth value provides a better gain and how it a�ects the 3-dB beamwidth in the E-plane.

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

14.2

14.3

14.4

14.5

14.6

14.7

14.8

14.9

15

15.1

15.2

Gai

n [d

Bi]

Gain vs Corrugations Depth Before the Aperture

Figure 3.2: Gain vs Corrugations depth before the aperture



50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

32

33

34

35

36

37

38

3-dB

Bea

mw

idth

[°]

Beamwidth vs Corugations Depth before the Aperture

Figure 3.3: 3-dB Beamwidth vs Corrugations depth before the aperture

In Figure 3.2 can be observed that when the depth of the corrugations increases from λ04 =

56.25 mm to λ02 = 112.25 mm, the gain also increases from 14.44 dB to 14.99 dB. For instance,

if the depths of the corrugations before the aperture are equal to 0.48λ0 = 108 mm, the gain willbe 14.98 dBi. As it can be seen in the Figure 3.3, as the depth increments, the -3dB beamwidthremains approxiamately constant.

Depth at the aperture

In this simulation it is proved that a quarter-wavelength corrugation depth at the aperture givesthe best results. For this purpose, a parameter sweep for the depth of the �rst corrugation fromλ04 to λ0

2 was done in order to study how it a�ects the gain and the beamwidth. The depths ofthe rest of the corrugations were not relevant in this case, so all were equaled to a random valueclosed to λ0

2 , 108 mm.



50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

14.5

14.55

14.6

14.65

14.7

14.75

14.8

14.85

14.9

14.95

15

Gai

n [d

Bi]

Gain vs Depth of the Corrugation at the Aperture

Figure 3.4: Gain vs Depth of the corrugations at the aperture

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

32

33

34

35

36

37

38

Bea

mw

idth

Beamwidth vs Depth of the Corrugation at the Aperture

Figure 3.5: 3-dB Beamwidth vs Depth of the corrugations at the aperture

As can be seen in Figure 3.4, the gain decreases from 14.9 dB when the depth is equal toλ04 , to 14.66 dB, when the depth value is λ0

2 . As shown in the Figure 3.5 there is no signi�cantvariation of the beamwidth respect to the depth.



Genetic Algorithm Optimization

An optimization using the genetic algorithm is performed for each depth starting with the secondone, in order to �nd out the corrugations depths that maximize the gain. The �rst corrugation'sdepth is �xed to λ0

4 = 56.25 mm and it will not be changed throughout this paper. The genetic

algorithm generates 5 random samples between a speci�ed range(λ04 to λ02 ) during 30 generations.

The �tness function calculates the value of a particular goal (in this case the value of the gain)for each generation and compares the results, keeping the ones which are more close to the goaland in the end, it converges to a global optimum. The results of the optimization can be foundin Appendix 3, in the Table 5.

The obtained gain is 14.96 dBi, not higher than the gain obtained before with all the depthsequal to each other. Therefore, it can be a�rmed that the global maximum was not found. Thegenetic algorithm may failed because the number of parameters was too large and the range wastoo high. A parameter sweep is performed next for each corrugation depth to study if a bettergain can be reached.

Step-by-step optimization

A parameter sweep from λ04 = 56.25 mm to λ0

2 = 112.5 mm was done for each corrugation'sdepth. The gain and the 3-dB beamwidth in the E-Plane are analized in order to observe theperformance of the system. In Appendix 2, the results for each corrugation can be found.

In summary, it was observed that the depths of the corrugations have di�erent impact onthe gain and on the beamwidth. For example, for the second corrugation, the gain and thebeamwidth remain approximately constant while the depth varies, as it can be observed inFigure 3.6.



50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

14.5

14.55

14.6

14.65

14.7

14.75

14.8

14.85

14.9

14.95

15

Gai

n [d

Bi]

Gain vs Depth of the Second Corrugation

(a) Gain with respect to Depth

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

32

33

34

35

36

37

38

Bea

mw

idth

[°]

Beamwidth vs Depth of the Second Corrugation

(b) Beamwidth with respect to Depth

Figure 3.6: Gain and Beamwidth of the second corrugation with respect to the Depth

However, for the twelfth corrugation, as it can be observed in Figure 3.7a, the gain increasesby 0.9 dBi while the depth increases, and the beamwidth decreases by 3.5°, while the depthincreases, as shown in Figure 3.7b.



50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

14.2

14.4

14.6

14.8

15

15.2

15.4

Gai

n [d

Bi]

Gain vs Depth of the Twelfth Corrugation

(a) Gain with respect to Depth

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

32

33

34

35

36

37

38

39

40

Bea

mw

idth

[°]

Beamwidth vs Depth of the Twelfth Corrugation

(b) Beamwidth with respect to Depth

Figure 3.7: Gain and Beamwidth of the twelfth corrugation with respect to the Depth

With the step-by-step tunning, the gain obtained is 15.67 dBi, while with the genetic opti-mization the gain obtained was 14.96 dBi. Next, the system with the maximum depth valuesfound is analyzed. In Figure 3.8 the re�ection coe�cient is illustrated. It can be observed thatthe system is matched between 1.21 GHz and 1.72 GHz, obtaining an approximate 510 MHzbandwidth.



1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2

Frequency [GHz]

-30

-25

-20

-15

-10

-5

0

S11

[dB

]

S11 Parameter

Figure 3.8: S11 Parameter

In the Figures 3.9, 3.10, 3.11 and 3.12 below, the radiation pattern of the antenna can beseen, at the central frequency 1.3 GHz and at edges of the band (1.21 GHz and 1.72 GHz). Itmust be considered that the polarization vector is on the y-axis. The E-plane is the YZ plane(θ variable and φ = 90°) and its copolar component is θ and its crosspolar component is φ. TheH-plane is the XZ plane (θ variable and φ = 0°) and its copolar and crosspolar components areφ and θ, respectively.

-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Dire

ctiv

ity [d

Bi]

Radiation pattern of the copolar component of the E-plane

1.21 GHz

1.3 GHz

1.72 GHz

Figure 3.9: Radiation pattern of the copolar component of the E-plane



-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-120

-110

-100

-90

-80

-70

-60

-50

-40

Dire

ctivity [d

Bi]

Radiation pattern of the crosspolar component of the E-plane

1.21 GHz1.3 GHz1.72 GHz

Figure 3.10: Radiation pattern of the crosspolar component of the E-plane

-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Dire

ctiv

ity [d

Bi]

Radiation pattern of the copolar component of the H-plane

1.21 GHz

1.3 GHz

1.72 GHz

Figure 3.11: Radiation pattern of the copolar component of the H-plane



-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-120

-110

-100

-90

-80

-70

-60

-50

-40

Dire

ctivity [

dB

i]

Radiation pattern of the crosspolar component of the H-plane

1.21 GHz1.3 GHz1.72 GHz

Figure 3.12: Radiation pattern of the crosspolar component of the H-plane

In Table 3.5 it can be seen the maximum gain, the side lobe level, the beamwidth at -3dBand at -10dB and the total e�ciency of the antenna, at the central frequency and at the extremefrequencies.

Table 3.5: Antenna Characteristics

FrequencyMaximum

Gain[dBi]

Side LobeLevel[dB]

3-dB

Beamwidth[°]

10-dB

Beamwidth[°]

Total

E�ciencyE-Plane H-Plane E-Plane H-plane E-Plane H-plane

1.21 GHz 13.32 -25.6 -27.7 43.7 41.2 73.70 74.75 88.31%

1.3 GHz 15.67 -13.8 -20.7 24.2 31 48.88 61.08 98.43%

1.72 GHz 14.75 -29 -29 29.3 25.6 88.55 45.42 91.76%

Second Genetic Algorithm Optimization

The �rst genetic algorithm may have failed because the search range was too wide. Following, asecond optimization for the depth of the corrugations has been done, this time using a smallerrange around the previously found values for each parameter. The obtained results can befound in Appendix 3, in Table 6. This time, the obtained gain is 15.62 dBi, higher than the gainobtained with the �rst genetic algorithm optimization.

In Figure 3.13 the re�ection coe�cient of the new system can be observed. The horn ismatched between 1.2 GHz and 1.77 GHz and the bandwidth is approximately 576 MHz, higherthan the bandwidth of the previous system. The radiation patterns for the central frequency andthe extremes frequencies are shown in Figures 3.14, 3.15, 3.16 and 3.17. As it can be observedin Figure 3.14, the corrugations do not work anymore for the higher frequency.



1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2

Frequency [GHz]

-30

-25

-20

-15

-10

-5

0

S11

[dB

]

S11 Parameter


-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Dire

ctiv

ity [d

Bi]


1.2 GHz

1.3 GHz

1.77 GHz




-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-120

-110

-100

-90

-80

-70

-60

-50

-40

Dire

ctiv

ity [d

Bi]


1.2 GHz1.3 GHz1.77 GHz


-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Dire

ctiv

ity [d

Bi]






-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-120

-110

-100

-90

-80

-70

-60

-50

-40

Dire

ctiv

ity [d

Bi]




The maximum gain, the side lobe level, the beamwidth at -3dB and at -10dB and the totale�ciency of the antenna at the central frequency and at the extreme frequencies are listed inTable 3.6.

Table 3.6: Antenna characteristics after optimization

FrequencyMaximum

Gain[dBi]

Side Lobe

Level[dB]

3-dB

Beamwidth[°]

10-dB

Beamwidth[°]

Total

E�ciencyE-Plane H-Plane E-Plane H-plane E-Plane H-plane

1.2 GHz 13.29 -27.6 -29 44.2 40.8 77.8 74 90.39%

1.3 GHz 15.62 -16 -22.9 26 31.9 52.4 62.6 99.01%

1.77 GHz 12.74 -15.9 -16.5 18.4 21 31.4 36.6 94.97%

In conclusion, after the optimization the gain variation is insigni�cant, as it decreased from15.67 dBi to 15.62 dBi. On the other hand, for the central frequency, the side lobe levels in theE-plane and in the H-plane are lower and the e�ciency is better, so from now on these depthvalues are going to be used in the next procedures.



3.3.2 Number of corrugations

The impact that the number of corrugations have on the horn is studied in this section. Inorder to achieve this aim, another two horns were designed: one with the minimmum numberof corrugations: 10, and another one with more corrugations than the original one: 14.

10-Corrugations Horn

The dimensions of the corrugations have been calculated as shown in Appendix 3 in Table 7.The width and the teeth of the corrugations have the same values as in the previous system,since they are the maximum values that allow the correct functioning of the system. As a �rstapproach, the depths are equal to the �rst 10 values found by the genetic algorithm.Figure 3.18 shows the re�ection coe�cient S11. There is matching between 1.16 GHz and 1.75GHz and the bandwidth is approximately 590 MHz. The radiation patterns for the centralfrequency and the extremes frequencies are shown in Figures 3.19, 3.20, 3.21 and 3.22. In Figure3.19 can be seen that the corrugations do not work for the highest frequency 1.75 GHz.

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2

Frequency [GHz]

-30

-25

-20

-15

-10

-5

0

S11

[dB

]

S11 Parameter




-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-80

-70

-60

-50

-40

-30

-20

-10

0

Dire

ctiv

ity [d

Bi]


1.16 GHz

1.3 GHz

1.75 GHz


-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-60

-50

-40

-30

-20

-10

0

10

20

Dire

ctiv

ity [d

Bi]


1.16 GHz

1.3 GHz

1.75 GHz




-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-80

-70

-60

-50

-40

-30

-20

-10

0

Dire

ctiv

ity [d

Bi]


1.16 GHz

1.3 GHz

1.75 GHz


-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

Dire

ctiv

ity [d

Bi]


1.16 GHz1.3 GHz1.75 GHz


In Table 3.7 the maximum gain, the side lobe levels, the -3dB and -10dB Beamwidths andthe total e�ciency are shown for the central frequency and the lowest and the highest frequenciesof the band:



Table 3.7: 10-corrugations horn characteristics before optimization

Side LobeLevel[dB]

3-dBBeamwidth

[°]

10-dBBeamwidth

[°]Frequency

Maximum

Gain[dBi] E-Plane H-Plane E-Plane H-plane E-Plane H-plane

Total

E�ciency

1.16 GHz 13.19 -25.5 -25.5 42 41.9 78.4 78.5 89.57%

1.3 GHz 15.62 -20.1 -19.8 29.5 29.2 58.8 58.4 100%

1.75 GHz 12.75 -17.8 -17.3 22.4 22 96.56 97.1 93.52%

14-Corrugations Horn

The dimensions of the 14-corrugations horn are shown in Appendix 3 in Table 9. The width andthe teeth of the corrugations are now lower, since the slant radius of the horn is the same andthere are more corugations than previoulsy. The depths of the �rst ten corrugations have beenequaled to the �rst ten optimized values found by the genetic algorithm for the 12-corrugationshorn. For the last two corugations depths, another genetic algorithm optimization was per-formed, and values obtained are shown in the Table 9.The re�ection parameter S11 is shown in Figure 3.23, where can be seen that the horn is matchedbetween 1.1 GHz and 1.72 GHz, obtaining a 620 MHz bandwidth. In Figures 3.24, 3.25, 3.26and 3.27 the radiation patterns of the E and H �elds can be seen. The corrugations do not workfor the highest frequency 1.72 GHz.

1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2

Frequency [GHz]

-40

-35

-30

-25

-20

-15

-10

-5

0

S11

[dB

]

S11 Parameter




-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Dire

ctiv

ity [d

Bi]


1.1 GHz

1.3 GHz

1.72 GHz


-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-60

-50

-40

-30

-20

-10

0

10

20

Dire

ctiv

ity [d

Bi]






-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Dire

ctiv

ity [d

Bi]




-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-60

-50

-40

-30

-20

-10

0

10

20

Dire

ctiv

ity [d

Bi]






Table 3.8: 14-corrugations horn characteristics

Side Lobe

Level[dB]

3-dB

Beamwidth[°]

10-dB

Beamwidth[°]

FrequencyMaximum

Gain[dBi] E-Plane H-Plane E-Plane H-plane E-Plane H-plane

Total

E�ciency

1.1 GHz 11.94 -14.2 -14.2 35.8 34.8 103.45 103.33 25.67%

1.3 GHz 15.68 -17.9 -17.5 28.3 28 56.82 56.40 85.05%

1.72 GHz 13.41 -4.6 -4.2 19.1 18.8 90.11 91.03 95.23%

In Table 3.8, the maximum gain, the side lobe levels, the -3dB and -10dB beamwidth in theE-plane and H-plane and the total e�ciency are shown.

Conclusions

To observe the in�uence that the number of corrugations have on the total performance of thesystem, the maximum gain, the side lobe levels, the -3dB and -10dB beamwidth in the E-planeand H-plane and the total e�ciency at the central frequency for the horns with 10, 12 and 14corrugations are summarized in Table 3.9.

Table 3.9: Horns characteristics

Number

ofCorrugations

Maximum

Gain[dBi]

Side Lobe

Level[dB]

3-dB

Beamwidth

[°]

10-dB

Beamwidth

[°]Total

E�ciency

E-Plane H-Plane E-Plane H-plane E-Plane H-plane

10 15.62 -20.1 -19.8 29.5 29.2 58.8 58.4 100%

12 15.62 -16 -22.9 26 31.9 52.4 62.6 99.01%

14 15.68 -17.9 -17.5 28.3 28 56.82 56.40 85.05%

As it can be observed in the table, the number of corrugations do not have a signi�cantin�uence on the gain. Regarding the side lobe level, the horn with 10 corrugations has thelowest side lobe level in the E-plane, the highest -3dB and -10dB beamwidths in the E-planeand the best e�ciency. The horn with 12 corrugations has the lowest side lobe level and thehighest -3dB and -10dB beamwidths in the H-plane.



3.4 Array Design

In this section an array is generated with each type of horn: 10-corrugations horn, 12-corruagtionshorn and 14-corrugations horn. For the �rst two horns, the optimized depths values were used,since they give a better performance to the system. The array is formed by four horns: two iny-axis and two in the z-axis. The elements must be placed side by side, so the distance betweencenters is the diameter of the aperture of the horn. First, the di�erence patterns of each arrayare shown, and then the sum patterns are compared with the TIRA sum patterns.

3.4.1 Array formed by four 10-corrugations horns

In the Figures below a comparison is made between the radiation patterns of the array formedby four 10-corrugations horns and the radiation patterns of the TIRA system, at the centralfrequency 1.3 GHz.

-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-80

-70

-60

-50

-40

-30

-20

-10

0

Dire

ctiv

ity [d

Bi]

Radiation pattern of the copolar component of the E-Plane

TIRA Reference10-Corrugations Horn

Figure 3.28: Radiation patterns of the copolar components of the E-plane of the horns arrayand the TIRA Reference



-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Dire

ctiv

ity [d

Bi]

Radiation pattern of the copolar component of the H-Plane


Figure 3.29: Radiation patterns of the copolar components of the H-plane of the horns arrayand the TIRA Reference

In Figures 3.28 and 3.29 can be observed that the radiation patterns of the corrugated hornhave more lobes than the TIRA reference. Some of them are visibly lower than the side lobesof the TIRA reference, and others are at the same level or higher. The radiation pattern has azero in 40°, where the side lobe of the TIRA pattern is located.





-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-80

-70

-60

-50

-40

-30

-20

-10

0

Dire

ctiv

ity [d

Bi]



Figure 3.30: Radiation pattern of the copolar components of the E-plane of the horns array andthe TIRA Reference

-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Dire

ctiv

ity [d

Bi]




In Figures 3.30 and 3.31 can be observed that some lobes of the 12-corrugations horn arelower than the side lobes of the TIRA reference. Comparing with the radiation pattern of the10-corrugations horn, the side lobes are higher.





-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Dire

ctiv

ity [d

Bi]



Figure 3.32: Radiation patterns of the copolar component of the E-plane of the horns array andthe TIRA Reference



-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 200

Theta [°]

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Dire

ctiv

ity [d

Bi]




In Figures 3.32 and 3.33 can be observed that the side lobe levels of the 14-corrugations hornare not lower than the side lobes of the TIRA radiation pattern.


4Conclusions

In conclusion, it was observed that the depth of the corrugations have a great e�ect on thesystem performance. The depth of a single corrugation can increase and decrease the gain orthe beamwidth and therefore the side lobe level. The number of corrugations do not a�ect thegain of the antenna, but less corrugations provide a better performance of the system.

Regarding the horns arrays, grating lobes were observed in the radiation patterns, as thedistance between elements is greater than λ0. The main goal of this thesis was to achieve lowerside lobes than the TIRA radiation pattern, and it was observed that with an array formed byfour horns with ten corrugations, lower side lobes can be reached.

To fully demonstrate that the corrugated horns array is better than the smooth-wall hornsarray, some of the next steps would be: match the zero beamwidth to the re�ector system,estimate the monopulse parameters and estimate safety limits.

41


42 CHAPTER 4. CONCLUSIONS

Bibliography

[1] Fraunhofer Institute.www.fhr.fraunhofer.de/en/the-institute/technical-equipment/space-observation-radar-tira.html.

[2] Merril I. Skolnik. Introduction to radar systems. pages 152�167, 2001.

[3] A. I. Leonov and K. I. Fomichev. Monopulse radar. pages 1�80, 1971.

[4] Ninoslav Majurec Davor Bonefacic, Julijana Jancula. Model of a monopulse radar trackingsystem for student laboratory. Radioengineering, VOL 16, NO. 3, pages 62�67, 2007.

[5] Dennis Kazako�. Aperture antennas. Antenna Theory and Applications, pages 153�188,2012.

[6] J. L. Masa Campos. Concepto antenas de apertura y antenas de bocina. pages 1�58, 2017.

[7] Constantine A. Balanis. Antenna theory. pages 783�791, 2005.

[8] Thomas A. Milligan. Modern antenna design. pages 336�379, 2005.

43


44 BIBLIOGRAPHY

Appendix 1: Corrugations Coordinate System

To calculate the coordinates of the corrugations it is important to consider β, the angle betweenthe center of the axis and the top of the corrugations, showed in Figure 1.

Figure 1: Cross section of the horn

Applying alternate angles it is possible to calculate the coordinate of each point of thecorrugations. In Figure 2 it is illustrated how the coordinates starting from the aperture havebeen calculated. It must be considered that t1 and t2 represent the teeths of the �rst and secondcorrugation, w1 is the width of the �rst corrugation and D1 and D2 are the depths of the �rstand second corrugation, respectively.

i


Figure 2: Coordinates of the �rst two corrugations.

The coordinates of the rest of the corrugations have been calculated in the same way. Theyare listed in Table 1 and shown in Figure 3.

ii APPENDIX . APPENDIX 1: CORRUGATIONS COORDINATE SYSTEM


Figure 3: Coordinates de�ned by points

APPENDIX . APPENDIX 1: CORRUGATIONS COORDINATE SYSTEM iii


Table 1: Coordinates of the 12 corrugations

PointCoordinates

PointCoordinates

X Y X Y

a0 0 0 a22 0 -D6

a1 t1 t1 tanβ a23 w6 0

a2 0 -D1 a24 0 D6 + w6 tanβ

a3 w1 0 a25 t7 t7 tanβ

a4 0 D1 + w1 tanβ a26 0 -D7


a6 0 -D2 a28 0 D7 + w7 tanβ

a7 w2 0 a29 t8 t8 tanβ

a8 0 D2 + w2 tanβ a30 0 -D8


a10 0 -D3 a32 0 D8 + w8 tanβ

a11 w3 0 a33 t9 t9 tanβ

a12 0 D3 + w3 tanβ a34 0 -D9

a13 t4 t4 tanβ a35 w9 0

a14 0 -D4 a36 0 D9 + w9 tanβ

a15 w4 0 a37 t10 t10 tanβ

a16 0 D4 + w4 tanβ a38 0 -D10

a17 t5 t5 tanβ a39 w10 0

a18 0 -D5 a40 0 D10 + w10 tanβ

a19 w5 0 a41 t11 t11 tanβ

a20 0 D5 + w5 tanβ a42 0 -D11

a21 t6 t6 tanβ a43 w11 0

a44 0 D11 + w11 tanβ a45 t12 t12 tanβ

a46 0 -D12

iv APPENDIX . APPENDIX 1: CORRUGATIONS COORDINATE SYSTEM


Then, the waveguide has been built considering that there must be a small distance betweenit and the last corrugation. First, a line which represents the length of the waveguide has beenadded(Figure 4a) and in order to give thickness to the horn the curve has been closed startingby the end point of this line(Figure 4b). Finally, for the aperture of the waveguide, a circlewhose radius is the radius of the waveguide has been attached at the end of the curve(Figure3c). In Figure 3, the coordinates of the points generated for each step mentioned above can beseen.

(a) Step 1: Coordinates of the points which form the waveguide length

(b) Step 2: Coordinates of the points which close the curve

APPENDIX . APPENDIX 1: CORRUGATIONS COORDINATE SYSTEM v


(c) Step 3: Aperture of the waveguide

Figure 3: Cross section of the waveguide

For closing the curve two new parameters have been de�ned: the thickness outer shell andthe angle α. The thickness_outer_shell is the length of the line parallel to the depth of thecorrugations, while α is the angle between the line perpendicular to the latter one and theexterior line at the bottom of the corrugations. Their values are shown in Table 2. In Figure 4the coordinates of the last point used for closing the curve can be seen.

Table 2: Auxiliary parameters

Parameter Value Units

thickness_outer_shell 120 mm

α 0.69 rad

Figure 4: Cross section of the aperture of the horn

vi APPENDIX . APPENDIX 1: CORRUGATIONS COORDINATE SYSTEM

Appendix 2: Step-by-step tuning

Second Corrugation Depth

A parameter sweep for the depth of the second corrugation has been done to �gure out whichdepth leads to the maximum gain. Its e�ects on the gain and on the beamwidth can be observedin the �gures below:

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

14.5

14.55

14.6

14.65

14.7

14.75

14.8

14.85

14.9

14.95

15

Ga

in [

dB

i]

Gain vs Depth of the Second Corrugation

Figure 5: Gain vs Depth of the second corrugation

vii


50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

32

33

34

35

36

37

38

Be

am

wid

th [

°]

Beamwidth vs Depth of the Second Corrugation

Figure 6: 3-dB Beamwidth vs Depth of the the second corrugation

The Figure 5 shows how the gain of the antenna varies as the depth of the second corrugationincreases. As the red line marks, the higher gain that can be obtained is 14.9132 dBi for a 102.5mm depth. In the Figure 6 is represented how the 3-dB beamwidth changes when the depth ofthe second corrugation increases. As it can be observed, the beamwidth variation respect to thedepth is not signi�cant. For a 102.5 mm depth, the beamwidth value is 34.88°.

Third Corrugation Depth

Previously it was demonstrated that a 102.5 mm second corrugation depth enhances the gain.Now is studied for which third corrugation depth, a higher gain can be obtained.

viii APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING


50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

14.5

14.6

14.7

14.8

14.9

15

15.1

Ga

in [

dB

i]

Gain vs Depth of the Third Corrugation

Figure 7: Gain vs Depth of the third corrugation

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

32

33

34

35

36

37

38

Be

am

wid

th [

°]

Beamwidth vs Depth of the Third Corrugation

Figure 8: 3-dB Beamwidth vs Depth of the third corrugation

As the red line indicates in Figure 7, the highest gain obtained is 15 dB for a 57.5 mm depth.Figure 8 shows that the beamwidth variation is not signi�cant and for a 57.5 mm depth, thebeamwidth is 34.85°.

APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING ix


Fourth Corrugation Depth

Another simulation has been performed in order to �nd out the depth of the fourth corrugationwhich maximizes the gain.

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

14.5

14.55

14.6

14.65

14.7

14.75

14.8

14.85

14.9

14.95

15

Ga

in [

dB

i]Gain vs Depth of the Fourth Corrugation

Figure 9: Gain vs Depth of the fourth corrugation

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

32

33

34

35

36

37

38

Bea

mw

idth

[°]

Beamwidth vs Depth of the Fourth Corrugation

Figure 10: 3-dB Beamwidth vs Depth of the fourth corrugation

x APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING


Figure 9 shows that the maximum gain obtained is 14.96 dB for 72.5 mm depth. Respectingthe beamwidth, this time it can be observed from Figure 10 that the beamwidth decreases asthe depth increments. For 72.5 mm depth, the beamwidth is 35.31°.

Fifth Corrugation Depth

At the beginning, the �rst corrugation's depth was �xed to 56.25 mm and the rest to 108 mm.A parameter sweep from λ0

4 = 56.25 mm to λ02 = 112.5 mm was done in a parallel way for the

second, third and fourth corrugations. To see if the total gain of the antenna has improved, thenext simulations are performed with the best depth values found for the �rst four corrugations.The depth values used in this simulations are showed in Table 3. A parameter sweep from λ0

4

to λ02 have been performed for the depth of the �fth corrugation to �nd out which value gives

the best gain.

Table 3: Depth values for the simulation


Depth of the �rst corrugation D1 56.25 mm

Depth of the second corrugation D2 102.5 mm

Depth of the third corrugation D3 57.5 mm

Depth of the fourth corrugation D4 72.5 mm

Depth of the sixth corrugation D6 108 mm

Depth of the seventh corrugation D7 108 mm

Depth of the eighth corrugation D8 108 mm

Depth of the ninth corrugation D9 108 mm

Depth of the tenth corrugation D10 108 mm

Depth of the eleventh corrugation D11 108 mm

Depth of the twelfth corrugation D12 108 mm

APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING xi


50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

13.5

13.7

13.9

14.1

14.3

14.5

14.7

14.9

15.1

15.3

15.515.6

Ga

in [

dB

i]

Gain vs Depth of the Fifth Corrugation

Figure 11: Gain vs Depth of the �fth corrugation

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

32

33

34

35

36

37

38

Be

am

wid

th [

°]

Beamwidth vs Depth of the Fifth Corrugation

Figure 12: 3-dB Beamwidth vs Depth of the �fth corrugation

As it can be observed in Figure 11, the gain increases when the depth is getting closer toλ2 = 112.5 mm and maximum gain obtained is 15.475 dBi. Therefore, a depth value close toa half-wavelength was choosen: 112 mm. In Figure 12 it can be observed that the beamwidthdecreases while the depth increments. For 112 mm depth, the beamwidth is approximately32.93°.

xii APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING


Sixth Corrugation Depth

This time a parameter sweep for the depth of the sixth corrugation from λ04 to λ0

2 has beenperformed.

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

14

14.2

14.4

14.6

14.8

15

15.2

15.4

15.6

Ga

in [

dB

i]Gain vs Depth of the Sixth Corrugation

Figure 13: Gain vs Depth of the sixth corrugation

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

32

33

34

35

36

37

38

Bea

mw

idth

[°]

Beamwidth vs Depth of the Sixth Corrugation

Figure 14: 3-dB Beamwidth vs Depth of the sixth corrugation

APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING xiii


Figure 13 shows that the gain increments when the depth increases. The value choosen forthe depth in this case is 112 mm, as it is pretty close to λ0

2 . The beamwidth in Figure 14decreases while the depth increments. For 112 mm depth, the 3-dB beamwidth is 32.84°.

Seventh Corrugation Depth

Likewise, another parametric sweep has been performed to �nd the seventh corrugation depththat maximizes the gain of the antenna.

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

14.6

14.7

14.8

14.9

15

15.1

15.2

15.3

15.4

15.5

15.6

Ga

in [

dB

i]

Gain vs Depth of the Seventh Corrugation

Figure 15: Gain vs Depth of the seventh corrugation

xiv APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING


50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

32

33

34

35

36

37

38

Be

am

wid

th [

°]

Beamwidth vs Depth of the Seventh Corrugation

Figure 16: 3-dB Beamwidth vs Depth of the seventh corrugation

As in the previous two simulations, Figure 15 shows that the gain increments while thedepth increases. The highest gain values can be obtained when the depth value is close tohalf-wavelength. Consequently the depth choosen is 112 mm. Respecting the 3-dB beamwidth,in Figure 16 it can been seen that the -3dB decreases while the depth increases and when thedepth es equal to 112 mm, the -3dB beamwidth is 32.79°.

Eighth Corrugation Depth

For this simulation, a parameter sweep from λ04 to λ0

2 has been performed in order to �nd outwhich depth for the eighth corrugation gives the highest gain.

APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING xv


50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

15

15.1

15.2

15.3

15.4

15.5

15.6

Ga

in [

dB

i]

Gain vs Depth of the Eighth Corrugation

Figure 17: Gain vs Depth of the eighth corrugation

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

30

31

32

33

34

35

36

37

38

Be

am

wid

th [

°]

Beamwidth vs Depth of the Eighth Corrugation

Figure 18: 3-dB Beamwidth vs Depth of the eighth corrugation

In Figure 17 is indicated that the highest gain obtained is 15.48 dBi for a 108.7 mm depth.As Figure 18 shows the beamwidth variation respect to the depth is not signi�cant and the -3dBbeamwidth which corresponds to this depth is 32.86°.

Ninth Corrugation Depth

Below, it is studied for which ninth corrugation depth, a higher gain can be obtained.

xvi APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING


50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

15.2

15.25

15.3

15.35

15.4

15.45

15.5

15.55

15.6

Ga

in [

dB

i]

Gain vs Depth of the Ninth Corrugation

Figure 19: Gain vs Depth of the ninth corrugation

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

30

31

32

33

34

35

36

37

38

Be

am

wid

th [

°]

Beamwidth vs Depth of the Ninth Corrugation

Figure 20: 3-dB Beamwidth vs Depth of the ninth corrugation

In Figure 19 is shown that the gain increments signi�cantly until 80 mm depth, then itremains approximately constant. The maximum peak can be observed for 98.75 mm depth,when the gain is 15.47 dBi. Regarding the -3dB beamwidth, its variation respect to the depthis not signi�cant, as it can be seen in Figure 20. For 98.75 mm depth, the -3dB beamwidth is32.91°.

APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING xvii


Tenth Corrugation Depth

For this simulation a parameter sweep has been performed in order to �nd out which tenthcorrugation depth gives the highest gain.

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

15.2

15.25

15.3

15.35

15.4

15.45

15.5

15.55

15.6

Ga

in [

dB

i]Gain vs Depth of the Tenth Corrugation

Figure 21: Gain vs Depth of the tenth corrugation

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

30

31

32

33

34

35

36

37

38

Be

am

wid

th [

°]

Beamwidth vs Depth of the Tenth Corrugation

Figure 22: 3-dB Beamwidth vs Depth of the tenth corrugation

xviii APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING


As it can be seen in Figure 21, the gain variation respect to the depth is not signi�cant.The maximum value obtained is 15.49 dBi for 77.5 mm depth. Figure 22 shows that the -dBbeamwidth remains approximately constant while the depth increments. If the tenth corrugationis 77.5 mm depth, the -3dB beamwidth will be 32.66°.

Eleventh Corrugation Depth

Another parameter sweep has been performed, this time for the depth of the eleventh corrugationfrom λ0

4 to λ02 .

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

15.2

15.25

15.3

15.35

15.4

15.45

15.5

15.55

15.6

Ga

in [d

Bi]

Gain vs Depth of the Eleventh Corrugation

Figure 23: Gain vs Depth of the eleventh corrugation

APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING xix


50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

30

31

32

33

34

35

36

37

38

Be

am

wid

th [

°]

Beamwidth vs Depth of the Eleventh Corrugation

Figure 24: 3-dB Beamwidth vs Depth of the eleventh corrugation

In Figure 23 it can be seen that the gain takes values between 15.4 and 15.5 dBi while thedepth increments from λ0

4 to λ02 . The maximum value obtained is 15.49 dBi, for 64.94 mm depth.

Figure 24 shows that the -3dB beamwidth variation respect to the depth is not signi�cant. Ifthe eleventh corrugation is 64.94 mm depth, the -3dB beamwidth will be 32.51°.

Twelfth Corrugation Depth

The last parameter sweep has been performed for depth of the twelfth corrugation, in order to�nd out which value of the depth maximizes the gain.

xx APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING


50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

14.2

14.4

14.6

14.8

15

15.2

15.4

Ga

in [

dB

i]

Gain vs Depth of the Twelfth Corrugation

Figure 25: Gain vs Depth of the twelfth corrugation

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Depth [mm]

32

33

34

35

36

37

38

39

40

Be

am

wid

th [

°]

Beamwidth vs Depth of the Twelfth Corrugation

Figure 26: 3-dB Beamwidth vs Depth of the twelfth corrugation

In Figure 25 it can be observed that the gain increments linearly while the depth increases.Consequently, a depth value close to a half-wavelength must be chosen, for instance 112 mm.Regarding the -3dB beamwidth, Figure 26 shows that it decreases signi�cantly while the depthincrements. For the chosen depth, its value is 34.79°.

APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING xxi


Conclusions and Results

Finally, in Table 4 the depths that maximize the gain of the antenna can be seen. In thesimulations performed, it was observed that for the �rst corrugation, the better depth value is0.25λ0. The depth of the second corrugation does not have a signi�cant impact on the gain,but a value close to 0.5λ0 makes it higher. The third and the fourth corrugations depths shouldbe close to 0.25λ0. For the next four corrugations, the depths should be as close as possible to0.5λ0. The depths of the corrugations number nine, ten and eleven must not be close to 0.25λ0,but between 0.3λ0 and 0.5λ0 their in�uence on the gain is not signi�cant. Finally, the depth ofthe last corrugation must be as close as possible to 0.5λ0.In conclusion, the depths of the corrugations close to the aperture must be around 0.25λ0, whilethe depths of the corrugations near the junction must be approximately 0.5λ0.Regarding the beamwidth, it was observed that for the �rst three corrugations, it remainsapproximately constant while the depths increase. From the fourth to the seventh corrugationand also for the last one, a decrease of maximum four degrees can be observed. Consequently,lower side lobes can be achieved if the depths of these corrugations are more close to 0.25λ0.From the eighth to the eleventh corrugations, the beamwidth does not have a signi�cant variationrespect to the depth.

Finally, in Table 6 the depths that maximize the gain of the antenna can be seen.

Table 4: Corrugations Depths

Corrugations Depth

First corrugation 56.25 mm

Second corrugation 102.5 mm

Third corrugation 57.5 mm

Fourth corrugation 72.5 mm

Fifth corrugation 112 mm

Sixth corrugation 112 mm

Seventh corrugation 112 mm

Eighth corrugation 108.71 mm

Ninth corrugation 98.75 mm

Tenth corrugation 77.5 mm

Eleventh corrugation 64.94 mm

Twelfth corrugation 112 mm

xxii APPENDIX . APPENDIX 2: STEP-BY-STEP TUNING

Appendix 3: Tables containing the values of the

depths of the corrugations

Table 5: Depths of the corrugations after the �rst genetic algorithm optimization


Depth of the second corrugation D2 66.39 mm

Depth of the third corrugation D3 80.88 mm

Depth of the fourth corrugation D4 71.66 mm

Depth of the �fth corrugation D5 96.54 mm

Depth of the sixth corrugation D6 105.82 mm

Depth of the seventh corrugation D7 92.80 mm

Depth of the eighth corrugation D8 80.53 mm

Depth of the ninth corrugation D9 77.73 mm

Depth of the tenth corrugation D10 85.19 mm

Depth of the eleventh corrugation D11 74.18 mm

Depth of the twelfth corrugation D12 110.15 mm

xxiii


Table 6: Corrugations Depths after the second genetic algorithm optimization

Corrugations Depth





Fifth corrugation 106.23 mm

Sixth corrugation 103.20 mm

Seventh corrugation 106.20 mm




Eleventh corrugation 73.48 mm

Twelfth corrugation 105.56 mm

xxivAPPENDIX . APPENDIX 3: TABLES CONTAINING THE VALUES OF THE DEPTHSOF THE CORRUGATIONS


Table 7: Corrugations dimensions for a 10-corrugations horn


Width of the corrugations wλ010 22.5 mm


Distance from the waveguide-horn junction distance Lc − (10w + 10t) 66.02 mm


Depth of the second corrugation D2 - 100.58 mm

Depth of the third corrugation D3 - 56.25 mm

Depth of the fourth corrugation D4 - 89.55 mm

Depth of the �fth corrugation D5 - 106.23 mm

Depth of the sixth corrugation D6 - 103.20 mm

Depth of the seventh corrugation D7 - 106.20 mm

Depth of the eighth corrugation D8 - 107.39 mm

Depth of the ninth corrugation D9 - 105.78 mm

Depth of the tenth corrugation D10 - 93.38 mm

APPENDIX . APPENDIX 3: TABLES CONTAINING THE VALUES OF THE DEPTHSOF THE CORRUGATIONS

xxv


Table 8: Depths of the 10 corrugations after optimization

Corrugations Depth





Fifth corrugation 102.44 mm

Sixth corrugation 98.68 mm

Seventh corrugation 110.80 mm




xxviAPPENDIX . APPENDIX 3: TABLES CONTAINING THE VALUES OF THE DEPTHSOF THE CORRUGATIONS


Table 9: Corrugations dimensions for a 14-corrugations horn


Width of the corrugations w 0.085λ0 19.12 mm


Distance from the waveguide-horn junction distance Lc − (14w + 14t) 18.99 mm


Depth of the second corrugation D2 - 100.58 mm

Depth of the third corrugation D3 - 56.25 mm

Depth of the fourth corrugation D4 - 89.55 mm

Depth of the �fth corrugation D5 - 106.23 mm

Depth of the sixth corrugation D6 - 103.23 mm

Depth of the seventh corrugation D7 - 106.20 mm

Depth of the eighth corrugation D8 - 107.39 mm

Depth of the ninth corrugation D9 - 105.78 mm

Depth of the tenth corrugation D10 - 93.38 mm

Depth of the eleventh corrugation D11 - 73.48 mm

Depth of the twelfth corrugation D12 - 105.56 mm

Depth of the thirteenth corrugation D13 - 87.01 mm

Depth of the fourteenth corrugation D14 - 57.13 mm

APPENDIX . APPENDIX 3: TABLES CONTAINING THE VALUES OF THE DEPTHSOF THE CORRUGATIONS

xxvii

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